Fractional Moment Methods for Anderson Localization in the Continuum

Details Fractional Moment Methods for Anderson Localization in the Continuum Fractional Moment Methods for Anderson Localization in the Continuum

2003-09-05

arxiv.org/abs/math-ph/0309018v1

Proceedings, Int. Cong. Math. Phys. (Lisbon 2003), (World Scientific, 2003).

Physics

Mathematical Physics

This is a brief announcement of math-ph/0308023, written for the proceedings of ICMP 2003

Scientific paper

The fractional moment method, which was initially developed in the discrete context for the analysis of the localization properties of lattice random operators, is extended to apply to random Schr\"odinger operators in the continuum. One of the new results for continuum operators are exponentially decaying bounds for the mean value of transition amplitudes, for energies throughout the localization regime. An obstacle which up to now prevented an extension of this method to the continuum is the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. This difficulty is resolved through an analysis of the resonance-diffusing effects of the disorder.

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